Normalization Property (abstract Rewriting)

In mathematical logic and theoretical computer science, a rewrite system has the strong normalization property (in short: the normalization property) if every term is strongly normalizing; that is, if every sequence of rewrites eventually terminates to a term in normal form. A rewrite system may also have the weak normalization property, meaning that for every term, there exists at least one particular sequence of rewrites that eventually yields a normal form.